That depends on how stiff your post is. I find it almost impossible on flies size 18 or below.
I tie parachutes, both big and small all the time.
Wrapping hackle on the post is much easier when the post is oriented parallel to the vise head.
I tie in the tail, post and body and finish the fly all the way the eye, whip finish and cut the thread tag.
I then rotate the fly 90* and orient the post parallel to the vise head (I prefer the fly rotated with the hook eye up so I can use the vise to rest my hand on when aligning the hackle feather).
I start my thread on the post the same as I would around the hook shank when starting a fly, and wind the thread up the post as far as I want the hackle to begin (I use fine thread for wrapping hackle for a neater job).
As mentioned above, you can put a little head cement on the base of the post to stiffen it up if necessary, but be sure make enough wraps on the post to lay down a good stiff base on the post for wrapping the hackle.
I then take my hackle feather stem, which is stripped of unwanted hackle fibers and wrap it to the post leaving a little extra stem exposed which allows me to orient the hackle properly. The tied in hackle stem in itself will add to the stiffness of the post for wrapping the hackle.
I begin to wrap the hackle down towards the base and tie off the hackle feather with a few thread wraps.
Sometimes I apply a little head cement to the thread, whip finish and cut off the tag of thread and trim off the end of the hackle feather.
Done!
I learned this method from a commercial tyer on a trip out-west back in the 80's and it has worked well for me for decades of tying parachute flies. I tie a lot of them since it's my favorite tie for most mayfly patterns.
Try it. With a little practice you will be able to tie parachutes well without any hassles or buying and things like a gallows tool or rotating hackle pliers.